PCN not on windscreen

Hello all,
I have come seeking some advice and best course of action in dealing with a parking ticket. I apologise in advance if I am not very coherent here, I am not well versed in these matters but hope you can see what I am trying to say here.

First I received a NTO from London Borough of Hounslow Council served on 02/08/2018 for a PCN I haven't seen as there was no PCN placed on windscreen of my car. I responded by appealing via post within the given time-frame of 28 days and was expecting a response that my appeal was either accepted or rejected but instead I have received a Charge Certificate with increased penalty to pay (£165). So it seems that my appeal letter did not reach them for some reason After receiving a Charge Certificate I filed an online appeal via the Council website explaining these circumstances but it was not accepted because I was late (outside of 28 days since the NTO was first issued).

In my online appeal I explained that no PCN was placed on my windscreen and so I was no aware that a PCN was issued in the first place and as the result I was not able to appeal it and pay for it at a discount rate of £55 should I accept it. You can see from the images in council system that no PCN was placed on my vehicle by the Enforcement Officer. And also from the images there is no evidence that I was parked at the place where I was allegedly parked as there is no markings or signs proving that my car is parked in a restricted area- there is a separate image of my car parked with no restricted signs or PCN visible, and there is another image with parking restriction sing but without my car in view. So I am not convinced that I was parked in the restricted area in the first place. Should I have found a PCN I would have paid it at a discounted rate if I am guilty but I was not given the chance and instead I received a NTO straight away representation for which was most likely lost in post and then I've got Charge Certificate instructing me to pay £165 which I believe I do not owe in the first place.

Council then sent me a letter saying that : " You were sent a NTO which gave you 28 days to either make Representations or pay. It also explained that if you did nothing the charge would increase from £110 to £165 and that you would be sent a Charge Certificate. I note your comments regarding appealing however our records show no Representations or payment were made and therefore a Charge Certificate has been issued. I must also advise that the Civil Enforcement Officer noted the return of the driver which is why more photographs were not taken. They also noted that the PCN was served by being handed to the driver. So I am satisfied the contravention occurred." My comment- the CEO did not hand me the PCN, nor did I see any CEO in the first place, they making it up, plain and simple.

Now Council says they will seek to recover the charge from me though Northampton County Court traffic Enforcement Centre.

Any thoughts on what can be done in these circumstances? Should I pay it or is there a way to fight it?
Apologies for the long post, I'd really appreciate any thoughts anyone might have from their own experiences or knowledge.

Thank you